Problem 4.163

# Problem 4.163 - Problem 4.163 [Difficulty: 4] Given: Rocket...

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Problem 4.163 [Difficulty: 4] Given: Rocket sled on track Find: Plot speed versus time; maximum speed; effect of reducing k Solution: Basic equation: Momentum flux in x direction Assumptions: 1) Steady flow 2) Incompressible flow 3) Atmospheric pressure in jet 4) Uniform flow (All in jet) Given data M 0 5000 kg = k5 0 Ns m = V e 1750 m s = M fuel 1000 kg = m rate 50 kg s = The momentum equation becomes F R a rf M u e m rate = V e m rate = and F R kU = From continuity MM 0 m rate t = Hence, combining k U M 0 m rate t () dU dt V e m rate = or dU dt V e m rate M 0 m rate t = Separating variables dU V e m rate dt M 0 m rate t = Integrating 1 k ln V e m rate ln V e m rate 1 m rate ln M 0 m rate t ln M 0 = Simplifying 1 k ln V e m rate V e m rate 1 k ln 1 V e m rate = 1 m rate ln M 0 m rate t M 0 = 1 m rate ln 1 m rate t M 0 = Solving for U Ut V e m rate k 11 m rate t M 0 k m rate = Using given data U10s ( ) 175 m s = and fuel is used up when

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## This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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Problem 4.163 - Problem 4.163 [Difficulty: 4] Given: Rocket...

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